A coherent subnanosecond single electron source Gwendal Fve
A coherent subnanosecond single electron source Gwendal Fève Groupe de Physique Mésoscopique Laboratoire Pierre Aigrain ENS Jean-Marc Berroir Bernard Plaçais Julien Gabelli Christian Glattli Adrien Mahé Takis Kontos Samples made at : Laboratoire de Photonique et Nanostructures (LPN) Yong Jin Bernard Etienne Antonella Cavana
Motivation Gaz 2 D I VG Weizmann Institute, Israel Y. Ji et al Nature 422 415 (2003) Poster P. Roulleau, CEA Saclay
Single electron sources D No temporal control Fano reduction factor DC biased Fermi sea is a noiseless electron source: 1 1, 0 ( . 6 0, 6 T 2 (1 - T 2 ) 1 + T 2 . 4 0, 4. 2 0, 2 0 0, 0 0. ) 1 - Tet 1 al. PRL (1996) Kumar . 8 0, 8 0. 5 1. 5 2. 5 Conductance 2 e² / h A. Kumar et al. Phys. Rev. Lett. 76 (1996) 2778. . Objective : realisation of a single electron source similar to single photon sources Time controlled injection of a single electron in a quantum conductor Electron optics with one or two electrons (entanglement…)
Principle of single charge injection QPC Boîte e D V(t) Gaz 2 D
Principle of single charge injection QPC Boîte e V(t) Gaz 2 D
Principle of single charge injection QPC Gaz 2 D Boîte e V(t) I V(t) t 100 ps for D=2. 5°K and D =0. 2
The quantum RC circuit l < mm
The quantum RC circuit Quantum dot D=t 2 No spin degeneracy One dimensional conductor
Linear dynamics of the quantum RC circuit Linear regime,
The quantum RC circuit, T=0 K CPQ , dot density of states The resistance is constant, independent of transmission, and equals half the resistance quantum for a single mode conductor ! M. Büttiker et al PRL 70 4114, PLA 180, 364 -369 (1993)
The quantum RC circuit , T=0 K Quantum dot D=t 2 • k. BT << DD Coherent regime • k. BT >> DD Sequential regime
Complex conductance D Fit by
Conclusion on linear dynamics linear regime: • dot spectroscopy • charge dynamics J. Gabelli, G. Fève et al Science 313 499 (2006) • complete determination of experimental parameters
Towards single charge injection Régime linéaire : Injection regime : Mean transferred charge Charge moyenne transférée by alternance : par alternance : The transferred charge is quantized
Current detection • In time domain : Fast averaging acquisition card Acquiris, Temporal resolution 500 ps. Developed by Adrien Mahé Slow excitation f=31. 25 MHz 16 odd harmonics of the current courant in a 1 GHz bandwidth « slow » dynamics • Measurement of the first harmonic : Faster excitation f=180 MHz and f=515 MHz More accurate determination of the transferred charge And of the escape time in the subnanoseond domain :
Time domain evolution of the current Average on 108 electrons
Response to a non-linear square excitation Simplification : • non-linear : First harmonic :
Response to a non-linear square excitation N(e) D • D<<1 , 1/D D» 1 e <<
First harmonic measurement 2 e. Vexc=3/2 D 2 e. Vexc=5/4 D 2 e. Vexc=3/4 D 2 e. Vexc=1/2 D 2 e. Vexc=1/4 D (linear regime)
Quantization of the AC current N(e)
Quantization of the AC current N(e)
Quantization of the AC current N(e)
Transmission dependence
Dot potential dependence f = 182 MHz N(e)
Escape time
Comparison with modelling
AC current diamonds 2 e. Vexc 0. 02 0. 15 0. 4 0. 8 0. 9 -897 -892 -887 Modelling : -912 -907 Im (Iw) (ef) -902 0 VG (m. V) 1 2 3 4 D
Conclusion • Quantization of the injected charge 1 st stage towards the realisation of a single electron source • Injection dyanmics measured in a large temporal range from 0. 1 to 10 ns • Excellent agreement with a simple modeling
Prospect • Electron-electron collision : Indistinguishibility of two independent sources
Experimental setup dc G=X+i. Y local 3 mm 3 cm rf
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